A058951 Coefficients of monic primitive irreducible polynomials over GF(7) listed in lexicographic order.

12, 14, 113, 123, 125, 135, 145, 153, 155, 163, 1032, 1052, 1062, 1112, 1124, 1152, 1154, 1214, 1242, 1262, 1264, 1304, 1314, 1322, 1334, 1352, 1354, 1362, 1422, 1432, 1434, 1444, 1504, 1524, 1532, 1534, 1542, 1552, 1564, 1604, 1612, 1632, 1644, 1654

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n=1..206 (through degree 4)

R. Church, Tables of irreducible polynomials for the first four prime moduli, Annals Math., 36 (1935), 198-209. Church's table extends through degree 3.

Mathematica

car = 7; maxDegree = 4;
okQ[coefs_List] := Module[{P}, P = coefs.x^Range[Length[coefs] - 1, 0, -1]; coefs[[1]] == 1 && IrreduciblePolynomialQ[P, Modulus -> car] && PrimitivePolynomialQ[P, car]];
FromDigits /@ Select[Table[IntegerDigits[k, car], {k, car+1, car^(maxDegree + 1)}], okQ] (* Jean-François Alcover, Sep 10 2019 *)

Crossrefs

Cf. A058946.

Irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058943, A058944, A058948, A058945, A058946. Primitive irreducible over GF(2), GF(3), GF(4), GF(5), GF(7): A058947, A058949, A058952, A058950, A058951.

Sequence in context: A337874 A337876 A058073 * A287916 A002926 A318298

Adjacent sequences: A058948 A058949 A058950 * A058952 A058953 A058954

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jan 13 2001

Extensions

More terms from Jean Gaumont (jeangaum87(AT)yahoo.com), Apr 16 2006

Status

approved